I just figured out how to do this and I have to say that I'm baffled how Reaper isn't like the only DAW on the market at this point, because it has a feature for just about anything you can imagine.
Apparently, you can use Reaper's built-in routing capability to process a dry signal with two (or more) completely different sets of plugins, on a single track.
All you have to do is make sure that the effects are receiving the dry signal instead of the signal processed by the previous effect, and then you can use for example your fifth effect to process the signal as if there were no plugins on the track before it.
I found this to be incredibly useful when creating a distorted bass guitar track, and I'll demonstrate how I did this in the example below.
I primarily use two effects when distorting bass, the fantastic JS plugin Bass Professor MK2 (this thing kicks serious ass on bass btw, you can find it in ReaPack) for the low end, and FabFilter Saturn (a multiband saturation plugin) for distorting the high end.
The thing is that I really don't like how these plugins work together, they just don't mix, so in the past I had to create separate tracks and blend them together to get the desired sound. With this trick, now I can do this on one track, and I really like to have a single track per instrument whenever it is possible.
First, you take your first effect, click on the routing button (the one next to "Param) and make sure that it is sending the input signal to inputs 3 and 4 ONLY (see pic below).
Then, take your second effect (for simplicity's sake I'm working with only 2 effects here but you can do it with as many as you wish), and using the same method, make sure that it is sending the signal to inputs 1 and 2 only.
Finally, you should add a third, transparent plugin (here I used ReaEQ but you can use anything that doesn't change your sound by default) and make sure that it is sending its inputs (the previous effects' outputs) from channels 1, 2, 3 and 4 to its set of outputs, 1 and 2.
This way, the output of the track will have the first effect on channels 3 and 4, the second effect on channels 1 and 2, they will all be audible but the signals will not mix, they will be independent. It's like having two tracks in one, and though it might seem simpler to just use two tracks, I find that it creates less work for me later on and I'm really thrilled that I discovered how to finally do this, so I don't have to clutter up my project with additional, unnecessary tracks. Hope this helps!
P.S. I originally wanted to post this to the Tips & Tricks thread, but since it's rather lengthy I figured that I'd just post it here. If that's not okay, feel free to delete this thread and I'll happily move the post into the sticky, I just felt that this would feel less cluttery.